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Sep 22, 2013
09/13

by
Z. C. Tu

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The maximum power of Feynman's ratchet as a heat engine and the corresponding efficiency ($\eta_\ast$) are investigated by optimizing both the internal parameter and the external load. When a perfect ratchet device (no heat exchange between the ratchet and the paw via kinetic energy) works between two thermal baths at temperatures $T_1> T_2$, its efficiency at maximum power is found to be $\eta_\ast =\eta_C^2 /[\eta_C-(1-\eta_C)\ln(1-\eta_C)]$, where $\eta_C\equiv 1-T_2/T_1$. This efficiency...

Source: http://arxiv.org/abs/0805.1482v3

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Sep 19, 2013
09/13

by
Z. C. Tu

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Only some special open surfaces satisfying the shape equation of lipid membranes can be compatible with the boundary conditions. As a result of this compatibility, the first integral of the shape equation should vanish for axisymmetric lipid membranes, from which two theorems of non-existence are verified: (i) There is no axisymmetric open membrane being a part of torus satisfying the shape equation; (ii) There is no axisymmetric open membrane being a part of a biconcave discodal surface...

Source: http://arxiv.org/abs/0909.0156v3

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Sep 23, 2013
09/13

by
Z. C. Tu

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This review reports some key results in theoretical investigations on configurations of lipid membranes and presents several challenges in this field which involve (i) exact solutions to the shape equation of lipid vesicles; (ii) exact solutions to the governing equations of open lipid membranes; (iii) neck condition of two-phase vesicles in the budding state; (iv) nonlocal theory of membrane elasticity; (v) relationship between symmetry and the magnitude of free energy.

Source: http://arxiv.org/abs/1212.5673v2

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Sep 21, 2013
09/13

by
Z. C. Tu

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The elastic, piezoelectric, electronic, and optical properties of a single ZnO monolayer (SZOML) with graphene-like structure are investigated from the first-principles calculations. The phonon dispersion curves contain three acoustic and three optical branches. At $\Gamma$ point, the out-of-plane acoustic mode has an asymptotic behavior $\omega (q)=Bq^2$ with $B=1.385 \times 10^{-7}$ m$^2$/s, while two in-plane acoustic modes have sound velocities $2.801$ km/s and $8.095$ km/s; the other three...

Source: http://arxiv.org/abs/0901.1112v3

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Sep 18, 2013
09/13

by
Z. C. Tu

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In this paper, spiral symmetry in cylindrical coordinate and general Bloch's theorem induced from it are discussed. This general Bloch's theorem is useful for considering the properties related to single-walled carbon nanotubes.

Source: http://arxiv.org/abs/cond-mat/0212003v1

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Sep 21, 2013
09/13

by
Z. C. TU

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This review reports some theoretical results on the Geometry of membranes. The governing equations to describe equilibrium configurations of lipid vesicles, lipid membranes with free edges, and chiral lipid membranes are derived from the variation of free energies of these structures. Some analytic solutions to these equations and their corresponding configurations are also shown.

Source: http://arxiv.org/abs/1106.2370v2

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Sep 23, 2013
09/13

by
Hao Wu; Z. C. Tu

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Shapes of planar lipid monolayer domains at the air-water interface are theoretically and numerically investigated by minimizing the formation energy of the domains which consist of the surface energy, line tension energy, and dipole electrostatic energy. The shape equation which describes boundary curves of the domains at equilibrium state is derived from the first order variation of the formation energy. A relaxation method is proposed to find the numerical solutions of the shape equation....

Source: http://arxiv.org/abs/0810.2000v2

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Sep 22, 2013
09/13

by
Z. C. Tu; X. Hu

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A new molecular motor is conceptually constructed from a double-walled carbon nanotube (DWNT) consisting of a long inner single-walled carbon nanotube (SWNT) and a short outer SWNT with different chirality. The interaction between inner and outer tubes is the sum of the Lennard-Jones potentials between carbon atoms in inner tube and those in outer one. Within the framework of Smoluchowski-Feynman ratchet, it is theoretically shown that this system in an isothermal bath will exhibit a...

Source: http://arxiv.org/abs/cond-mat/0501062v3

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Sep 21, 2013
09/13

by
Yang Wang; Z. C. Tu

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The efficiency at maximum power output of linear irreversible Carnot-like heat engines is investigated based on the assumption that the rate of irreversible entropy production of working substance in each "isothermal" process is a quadratic form of heat exchange rate between the working substance and the reservoir. It is found that the maximum power output corresponds to minimizing the irreversible entropy production in two "isothermal" processes of the Carnot-like cycle,...

Source: http://arxiv.org/abs/1108.2873v3

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Sep 23, 2013
09/13

by
Yang Wang; Z. C. Tu

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The efficiency at maximum power (EMP) of irreversible Carnot-like heat engines is investigated based on the weak endoreversible assumption and the phenomenologically irreversible thermodynamics. It is found that the weak endoreversible assumption can reduce to the conventional one for the heat engines working at maximum power. Carnot-like heat engines are classified into three types (linear, superlinear, and sublinear) according to different characteristics of constitutive relations between the...

Source: http://arxiv.org/abs/1110.6493v3

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0.0

Jun 30, 2018
06/18

by
Shiqi Sheng; Z. C. Tu

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We present a unified perspective on nonequilibrium heat engines by generalizing nonlinear irreversible thermodynamics. For tight-coupling heat engines, a generic constitutive relation of nonlinear response accurate up to the quadratic order is derived from the symmetry argument and the stall condition. By applying this generic nonlinear constitutive relation to finite-time thermodynamics, we obtain the necessary and sufficient condition for the universality of efficiency at maximum power, which...

Topics: Statistical Mechanics, Condensed Matter

Source: http://arxiv.org/abs/1404.7008

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Sep 23, 2013
09/13

by
Shiqi Sheng; Z. C. Tu

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A unified $\chi$-criterion for heat devices (including heat engines and refrigerators) which is defined as the product of the energy conversion efficiency and the heat absorbed per unit time by the working substance [de Tom\'{a}s \emph{et al} 2012 \textit{Phys. Rev. E} \textbf{85} 010104(R)] is optimized for tight-coupling heat engines and refrigerators operating between two heat baths at temperatures $T_c$ and $T_h(>T_c)$. By taking a new convention on the thermodynamic flux related to the...

Source: http://arxiv.org/abs/1212.6875v4

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0.0

Jun 28, 2018
06/18

by
Geng Li; Z. C. Tu

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The retainability of canonical distributions for a Brownian particle controlled by a time-dependent harmonic potential is investigated in the overdamped and underdamped situations, respectively. Because of different time scales, the overdamped and underdamped Langevin equations (as well as the corresponding Fokker-Planck equations) lead to distinctive restrictions on protocols maintaining canonical distributions. Two special cases are analyzed in details: First, a Brownian particle is...

Topics: Statistical Mechanics, Condensed Matter

Source: http://arxiv.org/abs/1511.01993

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Sep 18, 2013
09/13

by
Yang Wang; Z. C. Tu

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The Carnot-like heat engines are classified into three types (normal-, sub- and super-dissipative) according to relations between the minimum irreversible entropy production in the "isothermal" processes and the time for completing those processes. The efficiencies at maximum power of normal-, sub- and super-dissipative Carnot-like heat engines are proved to be bounded between $\eta_C/2$ and $\eta_C/(2-\eta_C)$, $\eta_C /2$ and $\eta_C$, 0 and $\eta_C/(2-\eta_C)$, respectively. These...

Source: http://arxiv.org/abs/1201.0848v2

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Sep 23, 2013
09/13

by
Z. C. Tu; X. Hu

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The elasticity and piezoelectricity of zinc oxide (ZnO) crystals and single layers are investigated from the first-principles calculations. It is found that a ZnO thin film less than three Zn-O layers prefers a planar graphite-like structure to the wurtzite structure. ZnO single layers are much more flexible than graphite single layers in the elasticity and stronger than boron nitride single layers in the piezoelectricity. Single-walled ZnO nanotubes (SWZONTs) can exist in principle because of...

Source: http://arxiv.org/abs/cond-mat/0511274v3

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Sep 18, 2013
09/13

by
Z. C. Tu; U. Seifert

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A theory of chiral lipid membranes is proposed on the basis of a concise free energy density which includes the contributions of the bending and the surface tension of membranes, as well as the chirality and orientational variation of tilting molecules. This theory is consistent with the previous experiments [J.M. Schnur \textit{et al.}, Science \textbf{264}, 945 (1994); M.S. Spector \textit{et al.}, Langmuir \textbf{14}, 3493 (1998); Y. Zhao, \textit{et al.}, Proc. Natl. Acad. Sci. USA...

Source: http://arxiv.org/abs/0705.2707v2

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Jun 26, 2018
06/18

by
Shiqi Sheng; Z. C. Tu

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Typical heat engines exhibit a kind of homotypy: The heat exchanges between a cyclic heat engine and its two heat reservoirs abide by the same function type; the forward and backward flows of an autonomous heat engine also conform to the same function type. This homotypy mathematically reflects in the existence of hidden symmetries for heat engines. The heat exchanges between the cyclic heat engine and its two reservoirs are dual under the joint transformation of parity inversion and...

Topics: Condensed Matter, Statistical Mechanics

Source: http://arxiv.org/abs/1501.03563

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Sep 20, 2013
09/13

by
Z. C. Tu; Z. C. Ou-Yang

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An elegant formula for coordinates of carbon atoms in a unit cell of a single-walled nanotube (SWNT) is presented and a new molecular motor of double-walled carbon nanotube whose inner tube is a long (8,4) SWNT and outer tube a short (14,8) SWNT is constructed. The interaction between inner an outer tubes is analytically derived by summing the Lennard-Jones potentials between atoms in inner and outer tubes. It is proved that the molecular motor in a thermal bath exhibits a directional motion...

Source: http://arxiv.org/abs/cond-mat/0301511v4

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Sep 19, 2013
09/13

by
Z. C. Tu; Z. C. Ou-Yang

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An elegant formula for coordinates of carbon atoms in a unit cell of a single-walled nanotube (SWNT) is presented and the potential of neon (Ne) inside an infinitely long SWNT is analytically derived out under the condition of the Lennard-Jones potential between Ne and carbon atoms. Specific heats of dilute Ne inside long (20, 20) SWNT are calculated at different temperatures. It is found that Ne exhibits 3-dimensional (3D) gas behavior at high temperature but behaves as 2D gas at low...

Source: http://arxiv.org/abs/cond-mat/0303286v3

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Sep 22, 2013
09/13

by
Z. C. Tu; Z. C. Ou-Yang

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The purpose of this paper is to study the shapes and stabilities of bio-membranes within the framework of exterior differential forms. After a brief review of the current status in theoretical and experimental studies on the shapes of bio-membranes, a geometric scheme is proposed to discuss the shape equation of closed lipid bilayers, the shape equation and boundary conditions of open lipid bilayers and two-component membranes, the shape equation and in-plane strain equations of cell membranes...

Source: http://arxiv.org/abs/cond-mat/0403309v3

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Sep 20, 2013
09/13

by
Z. C. Tu; Z. C. Ou-Yang

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After a brief introduction to several variational problems in the study of shapes of thin thickness structures, we deal with variational problems on 2-dimensional surface in 3-dimensional Euclidian space by using exterior differential forms. The morphological problems of lipid bilayers and stabilities of cell membranes are also discussed. The key point is that the first and the second order variations of the free energy determine equilibrium shapes and mechanical stabilities of structures.

Source: http://arxiv.org/abs/math-ph/0506055v3

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Sep 22, 2013
09/13

by
Z. C. Tu; Z. C. Ou-Yang

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The structures and symmetries of single-walled carbon nanotubes (SWNTs) are introduced in detail. The physical properties of SWNTs induced by their symmetries can be described by tensors in mathematical point of view. It is found that there are 2, 4, and 5 different parameters in the second, third, and fourth rank tensors representing electronic conductivity (or static polarizability), the second order nonlinear polarizability, and elastic constants of SWNTs, respectively. The values of elastic...

Source: http://arxiv.org/abs/cond-mat/0205544v3

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Sep 17, 2013
09/13

by
Z. C. Tu; Z. C. Ou-Yang

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Lipid membrane with freely exposed edge is regarded as smooth surface with curved boundary. Exterior differential forms are introduced to describe the surface and the boundary curve. The total free energy is defined as the sum of Helfrich's free energy and the surface and line tension energy. The equilibrium equation and boundary conditions of the membrane are derived by taking the variation of the total free energy. These equations can also be applied to the membrane with several freely...

Source: http://arxiv.org/abs/cond-mat/0305700v4

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0.0

Jun 30, 2018
06/18

by
Shiqi Sheng; Pan Yang; Z. C. Tu

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The \chi-criterion is defined as the product of the energy conversion efficiency and the heat absorbed per-unit-time by the working substance [de Tom\'as et al., Phys. Rev. E, 85 (2012) 010104(R)]. The \chi-criterion for Feynman ratchet as a refrigerator operating between two heat baths is optimized. Asymptotic solutions of the coefficient of performance at maximum \chi-criterion for Feynman ratchet are investigated at both large and small temperature difference. An interpolation formula, which...

Topics: Statistical Mechanics, Condensed Matter

Source: http://arxiv.org/abs/1402.6447

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Sep 18, 2013
09/13

by
Z. C. Tu; Z. C. Ou-Yang

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A Comment on the Letter by Granger et.al., Phys. Rev. Lett. 89, 135506 (2002).

Source: http://arxiv.org/abs/cond-mat/0212008v1

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Jul 20, 2013
07/13

by
Z. C. Tu; Z. Y. Wan

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First, we extend the special relativity into the superluminal case and put forward a superluminal theory of kinematics, in which we show that the temporal coordinate need exchanging with one of the spatial coordinates in a superluminal inertial frame, and that the coordinate transformations from any superluminal inertial frame to the rest frame (here rest just says in a relative sense) are the same as the Lorentz transformations from some normal inertial frame to the rest frame. Consequently,...

Source: http://arxiv.org/abs/physics/0107032v3

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Sep 21, 2013
09/13

by
Z. C. Tu; Z. C. Ou-Yang

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This review presents the elastic theory of low-dimensional (one- and two-dimensional) continua and its applications in bio- and nano-structures. First, the curve and surface theory, as the geometric representation of the low-dimensional continua, is briefly described through Cartan moving frame method. The elastic theory of Kirchhoff rod, Helfrich rod, bending-soften rod, fluid membrane, and solid shell is revisited. Secondly, the application and availability of the elastic theory of...

Source: http://arxiv.org/abs/0706.0001v2

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Sep 19, 2013
09/13

by
Z. C. Tu; Z. C. Ou-Yang

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Based on the van der Waals interaction, the periodically nonlinear potential of a singe-walled carbon nanotube (SWNT) with finite length in an infinite length SWNT is analytically obtained. It is found that the inner SWNT can oscillate in the outer SWNT with frequency beyond ten Gigahertz, even up to a hundred Gigahertz.

Source: http://arxiv.org/abs/cond-mat/0302458v1

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Sep 19, 2013
09/13

by
Z. C. Tu; Q. X. Li; X. Hu

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The formation of ZnO nanorings and nanohelices with large polar surfaces observed in experiments [Nano Lett. 3, 1625 (2003); J. Am. Chem. Soc. 126, 6703 (2004)] is shown to be a result of the competition between elastic energy, spontaneous polarization-induced surface energy, volume energy, and defect-induced energy. It is found that nanorings and nanohelices observed in experiments are stable and energetically favorable structures.

Source: http://arxiv.org/abs/cond-mat/0507321v2

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Sep 22, 2013
09/13

by
Z. C. Tu; R. An; Z. C. Ou-Yang

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A cell membrane can be simply regarded as composite material consisting of lipid bilayer, membrane cytoskeleton beneath lipid bilayer, and proteins embedded in lipid bilayer and linked with membrane cytoskeleton if one only concerns its mechanical properties. In this Chapter, above all, the authors give a brief introduction to some important work on mechanical properties of lipid bilayers following Helfrich's seminal work on spontaneous curvature energy of lipid bilayers. Next, the entropy of a...

Source: http://arxiv.org/abs/q-bio/0501001v1

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Jun 29, 2018
06/18

by
Y. H. Zhang; Z. McDargh; Z. C. Tu

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The shape equation of lipid membranes [Zhong-can and Helfrich(1987) PRL 59 2486] is a fourth-order partial differential equation. Under the axisymmetric condition, this equation was transformed into a second-order ordinary differential equation (ODE) by Zheng and Liu [Zheng and Liu(1993) PRE 48 2856]. Here we try to further reduce this second-order ODE to a first-order ODE by seeking for first integrals according to the Noether theorem. We indeed find a first integral when the second-order ODE...

Topics: Soft Condensed Matter, Mathematical Physics, Condensed Matter, Mathematics

Source: http://arxiv.org/abs/1611.07747

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Sep 23, 2013
09/13

by
Z. C. Tu; L. Q. Ge; J. B. Li; Z. C. Ou-Yang

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The entropy of a polymer confined in a curved surface and the elastic free energy of a membrane consisting of polymers are obtained by scaling analysis. It is found that the elastic free energy of the membrane has the form of the in-plane strain energy plus Helfrich's curvature energy [Z. Naturforsch. C \textbf{28}, 693 (1973)]. The elastic constants in the free energy are obtained by discussing two simplified models: one is the polymer membrane without in-plane strains and asymmetry between...

Source: http://arxiv.org/abs/cond-mat/0312319v6

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Sep 20, 2013
09/13

by
Yang Wang; Mingxing Li; Z. C. Tu; A. Calvo Hernández; J. M. M. Roco

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The figure of merit for refrigerators performing finite-time Carnot-like cycles between two reservoirs at temperature $T_h$ and $T_c$ ($

Source: http://arxiv.org/abs/1205.2258v2